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High School Math Calculus Calculus: Graphical, Numerical, Algebraic

The velocity at which you hit the water if you step off from 10 m diving platform.

The velocity at which you hit the water if you step off from 10 m diving platform.

Calculus: Graphical, Numerical, Algebraic

Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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Question

Chapter 5.2, Problem 44E

(a)

To determine

To find: The velocity at which you hit the water if you step off from 10 m diving platform.

(a)

Expert Solution

Answer to Problem 44E

Explanation of Solution

Calculation:

Consider the velocity of the body under the free fall is,

v(t)=9.8t+C

Since, the position function is the ant derivative of the velocity so the t=0 and C=0 .

Then, the distance is,

s(t)=9.8(12)t2+C=4.9t2

Then, for the height of the 10 m distance is,

10=4.9t2t=1.43 s

Then, the velocity is,

v(t)=9.8(1.43)+0=14 m/s

(b)

To determine

To find: The velocity at which you hit the water if you dive off the platform with the upward velocity of 2 m per sec.

(b)

Expert Solution

Answer to Problem 44E

The velocity of the person is 14.14 m/s .

Explanation of Solution

Calculation:

Consider the initial velocity is -2 m/s and consider the downward as the positive.

Consider the positive function changes and the value of C=0 as the position is 0 at t=0 .

Then, the equation of the distance is,

s(t)=4.9t2−2t10=4.9t2−2tt=−(−2)±(−2)2−4(4.9)(−10)2(4.9)t=1.65,−1.24

Then, the velocity is,

v(1.65)=9.8(1.65)−2=14.14 m/s

Chapter 5.2, Problem 43E

Chapter 5.2, Problem 45E

Chapter 5 Solutions

Calculus: Graphical, Numerical, Algebraic

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